In post 90, Elements wrote:In regards to weather the mafia would put themselves at the top or bottom of the list - I think there's so much wifom there it's pointless speculating especially given we can get anyone to the top of the list.
So there is one thing I'd like to discuss about this.
So back when I was teaching this subject at MIT - this was back in 2007 - I conducted a small experiment.
I told one group of students to flip a coin 100 times, and note down the resulting sequence of Heads and Tails flips.
I told a second group of students to write down what they
thought
a 100 long sequence of random coin flips would look like.
I walked out of the room and allowed each group to write down their sequences. They wrote them down on individual pieces of paper.
When I returned, they handed me the two sequences, I did not know which sequence corresponded to which group.
Yet, it took me all of 3 seconds to determine which sequence was the fabricated one.
Why?
Because humans don't understand how true randomness
really
works.
The fabricated list's longest run of consecutive Head/Tail flips was 4. 4 Head flips in a row.
The
real list
had a run of
7
Tail flips in a row.
That's all it took for me to determine the true sequence.
The students fabricating the list thought it'd be ridiculous to have any more than 4 Heads in a row, I'd spot it's fake otherwise, right?
Wrong.
True randomness will result in much longer sequences of Heads/Tails.
In addition, the fabricated list just had smaller consecutive runs in general, the real one didn't.
So now that you're up to date with number theory, how do we apply it to this game?
Well.
The two mafia are very unlikely to pick two numbers very close together, and are extremely unlikely to pick the same number.
They avoid this since they believe their similar numbers could be used to link them together, that it wouldn't look natural if they were so close.
But in reality? Randomness doesn't give a damn about that.
So we can use this logic to not completely discount but make some scum teams far less likely.
Me and Dunn? Extremely unlikely. However, this doesn't apply here since I'm a master of Number Theory.
Azure and Nymph? Very unlikely.
Locke and Nymph? Relatively unlikely.
Same goes for pops with Azure.
And for Elements and Dongempire, and Dongempire and pops since the difference is proportionally smaller at those numbers.
Feel free to ask any questions. My students always had plenty after my regular lectures.